Three-Dimensional Transient Electromagnetic Forward Modeling for Simulating Arbitrary Source Waveform Using Convolution Approach

Abstract

The transient electromagnetic (TEM) method utilizes artificial transmitters and measures electromagnetic responses to reveal the resistivity information of the subsurface. The current waveform of transmitters has non-negligible effects on induced fields. Therefore, 3-D TEM forward modelling algorithms need the capability of simulating arbitrary waveforms to obtain accurate responses. In time-stepping-based 3-D TEM forward modelling, the source term approach is frequently used, which employs the source current density to model the waveform variation during time-stepping. The source term approach, however, requires fine-time discretization to describe complex waveforms, which could significantly raise the computational cost. We present a robust convolution approach that computes the convolution between the time derivative of the waveform and the step-off response to incorporate the waveform effects in 3-D TEM modelling. The convolution approach does not discretize the waveform using time steps. Hence, it is advantageous when modelling full-waveform cases. The developed algorithm is based on the finite-element method using unstructured grids and the implicit backward Euler approach. Both galvanic and inductive transmitters are incorporated. Ground and airborne TEM surveys are tested using an actual airborne TEM waveform, a full waveform of the 2( <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>n</i></sup> )-sequence pseudo-random signal, and various synthetic waveforms. Accuracy is validated against the 1-D and 3-D solutions of published studies. The source term and convolution approaches are compared. Synthetic examples show that the latter approach simplifies the waveform incorporation in TEM modelling and substantially improves time-stepping efficiency without sacrificing accuracy.